Alena Blinova

Antonina Plaskovitskaya

We analyse data on the signs for verbs in the Russian sign language. There are 436 observations, each signifying a specific sign. Signs are described according to 13 aspects: - finger selection - the fingers that take part in the shape or movement; - aperture - the position of the thumb against the other selected fingers, both static and dynamic; - curve - the way fingers are bent in distal joints, both static and dynamic; - bent - the way fingers are bent in proximal joints, both static and dynamic; - facing orientation - orientation of the hand towards the place where the sign takes place; - focus orientation - orientation of the hand along the direction of movement; - width - distance between selected fingers, both static and dynamic; - dynamic orientation - turn or bend of the wrist; - location - point where the sign takes place; - plane - plane in which the sign takes places; - settings - start and end points of the movement trajectory; - path - form of the movement trajectory; - manner - aspects of the sign modifying other factors.

All the variable within the dataseet are categorical: the values are nominal and cannot be ordered in a sensible way. Therefore, we are limited with the choice of analysis methods to correspondence analysis, multiple correspondence analysis, chi-square, and Fisher’s exact test.

The summary for frequencies of parameter values looks as follows:

## ── Attaching packages ─────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 2.2.1     ✔ purrr   0.2.4
## ✔ tibble  1.4.2     ✔ dplyr   0.7.4
## ✔ tidyr   0.7.2     ✔ stringr 1.2.0
## ✔ readr   1.1.1     ✔ forcats 0.2.0
## ── Conflicts ────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## Loading required package: grid
##    H1.FingerSelection      H1.Aperture             H1.Curve  
##  all        :195      absent     :320   absent         : 43  
##  1-st       :113      closed     : 35   curved         : 65  
##  1-st; 2-nd : 54      closed-open: 19   curved-straight: 13  
##  absent     : 34      open       : 19   straight       :281  
##  1-st; thumb: 11      open-closed: 43   straight-curved: 34  
##  1-st; 4-th :  7                                             
##  (Other)    : 22                                             
##           H1.Bent     H1.Facing     H1.Focus                    H1.Width  
##  absent       : 58   absent: 27   absent: 39   absent               :182  
##  bent         : 63   back  : 42   back  : 49   pointed              :155  
##  bent-straight: 21   palm  :142   palm  : 63   pointed-wide         :  8  
##  straight     :271   radial: 33   radial: 33   pointed; pointed-wide:  1  
##  straight-bent: 23   root  : 25   root  : 21   wide                 : 73  
##                      tips  :113   tips  :175   wide-pointed         : 17  
##                      ulnar : 54   ulnar : 56                              
##      Dynamic.Orientation                  Location          Plane    
##  absent        :381      space                :160   absent    :112  
##  prone-neutral : 16      hand-palm            : 72   horisontal:237  
##  supine-prone  : 13      trunk                : 28   parallel  : 48  
##  prone-supine  : 10      head-high            : 25   sagittal  : 39  
##  neutral-prone :  7      head-low             : 21                   
##  neutral-supine:  5      virtual object; space: 19                   
##  (Other)       :  4      (Other)              :111                   
##          Settings             Path                  H2.FingerSelection
##  far-near    : 78   sraight     :274   1-st                  :  1     
##  proxi-distal: 61   arc         : 83   1-st; 2-nd; 3-rd; 4-th:  2     
##  high-low    : 39   absent      : 40   1-st; 4-th            :  1     
##  absent      : 36   vawe        : 14   absent                :427     
##  low-high    : 35   iconic      : 10   thumb                 :  5     
##  ipsi-contra : 33   circle-clock:  5                                  
##  (Other)     :154   (Other)     : 10                                  
##  H2.Aperture      H2.Curve       H2.Bent       H2.Width    H2.Facing  
##  absent:435   absent  :430   absent  :430   absent :434   absent:373  
##  open  :  1   curved  :  1   straight:  6   pointed:  2   back  : 36  
##               straight:  5                                palm  : 20  
##                                                           ulnar :  7  
##                                                                       
##                                                                       
##                                                                       
##    H2.Focus                                  Manner     H1.Focus_2 
##  absent:435   absent                            :120         :426  
##  tips  :  1   symmetrical                       : 95   radial:  1  
##               repeated                          : 59   root  :  1  
##               tense                             : 30   tips  :  3  
##               repeated; symmetrical             : 21   ulnar :  5  
##               repeated; symmetrical; alternating: 17               
##               (Other)                           : 94               
##  H1.Facing_2 
##        :423  
##  absent:  1  
##  back  :  2  
##  palm  :  2  
##  radial:  4  
##  ulnar :  4  
## 

There are many values marked as absent. The reason for this is that, for many signs, some categories are present, and then they get corresponding meanings. Some, in turn, are not, e.g. no fingers are selected, and an absence of category marker for the specific sign can be seen as a separate value in itself.

We focus mainly on the aspects belonging to the node Active Articulator (https://docs.google.com/document/d/1Kd5qAFEwhJ4ZB7Dh96kfyTa_w4tjFekHgutL1_K1PUg/edit, Plaskovitskaya 2018). This scheme is derived from dependency model introduced by Els van der Kooij (2002). We expect to discover dependencies within this node, especially between items of different levels; however, we do not expect to exclude all dependent nodes. Our expectation is that some parameters within a sign (e.g. its aperture) may be connected with some other parameters (e.g. focus orientation); the direction of this relationship, if any, is not clear. However, general linguistic considerations suggest that the dependent nodes are influenced by the top ones - in this case, orientation depends on the aperture which is included in the top hand configuration node. Therefore, the hypotheses to be tested are those regarding interdependence; the actual factors analysed out of the given 13 are to be defined below.

In order to explore the data, we use correspondence analysis. It helps to discover the systematic patterns of variations with categorical data which we have here. It looks the following way for Curve and Bent:

library(FactoMineR)
## Warning: package 'FactoMineR' was built under R version 3.4.4
curve_bent_data = dict_output[, c(4, 5)]
CB.contingency_table = table(curve_bent_data$H1.Curve, curve_bent_data$H1.Bent)
CB.res.ca = CA(CB.contingency_table, graph=FALSE)
summary(CB.res.ca)
## 
## Call:
## CA(X = CB.contingency_table, graph = FALSE) 
## 
## The chi square of independence between the two variables is equal to 530.1564 (p-value =  1.415047e-102 ).
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4
## Variance               0.682   0.287   0.246   0.001
## % of var.             56.069  23.633  20.245   0.053
## Cumulative % of var.  56.069  79.701  99.947 100.000
## 
## Rows
##                   Iner*1000     Dim.1     ctr    cos2     Dim.2     ctr
## absent          |   552.016 |   2.319  77.797   0.961 |  -0.258   2.276
## curved          |    12.851 |  -0.016   0.006   0.003 |  -0.149   1.152
## curved-straight |   288.107 |   0.954   3.978   0.094 |   2.836  83.431
## straight        |   127.066 |  -0.429  17.357   0.931 |   0.026   0.156
## straight-curved |   235.916 |   0.274   0.862   0.025 |  -0.692  12.985
##                    cos2     Dim.3     ctr    cos2  
## absent            0.012 |  -0.391   6.115   0.027 |
## curved            0.258 |  -0.245   3.649   0.699 |
## curved-straight   0.832 |   0.844   8.624   0.074 |
## straight          0.004 |  -0.113   3.325   0.064 |
## straight-curved   0.158 |   1.572  78.288   0.817 |
## 
## Columns
##                   Iner*1000     Dim.1     ctr    cos2     Dim.2     ctr
## absent          |   560.883 |   2.022  79.738   0.969 |  -0.080   0.299
## bent            |    29.895 |  -0.421   3.749   0.855 |  -0.040   0.081
## bent-straight   |   270.444 |   0.239   0.404   0.010 |   2.231  83.453
## straight        |   107.518 |  -0.395  14.236   0.903 |  -0.069   1.041
## straight-bent   |   247.216 |   0.492   1.873   0.052 |  -0.908  15.127
##                    cos2     Dim.3     ctr    cos2  
## absent            0.002 |  -0.351   6.661   0.029 |
## bent              0.008 |  -0.158   1.457   0.120 |
## bent-straight     0.887 |   0.761  11.324   0.103 |
## straight          0.028 |  -0.109   2.982   0.068 |
## straight-bent     0.176 |   1.903  77.577   0.773 |

Looking at the data, we see that the first two dimensions reflect nearly all inertia; therefore, three dimensions are enough. What is more, basically two values per dimension explain the majority of the variation. Therefore, we first plot the first two dimensions:

and then the second and the third:

Next, we plot the points that are best represented in the new space:

We see that all the columns are correlated for the two variables, Curve and Bent, therefore, we can retain only one of the two for further analysis (for particular calues, there is high probability that they are phonetical variations of each other). As Curve, in opposition to Bent, differs between bent and straight static positions, it is better to keep Curve (rather than Bent) in the phonological model.

In order to test once more the hypothesis that Curve and Bent are correlated, we apply Fisher’s Exact Test (as chi-square test indicates it may give wrong results):

#H1.Bent~H1.Curve
new_table10=table(dict_output$H1.Bent, dict_output$H1.Curve)
chisq.test(new_table10)
## Warning in chisq.test(new_table10): Chi-squared approximation may be
## incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  new_table10
## X-squared = 530.16, df = 16, p-value < 2.2e-16
fisher.test(CB.contingency_table, simulate.p.value = TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  CB.contingency_table
## p-value = 0.0004998
## alternative hypothesis: two.sided
assocstats(CB.contingency_table)
##                     X^2 df P(> X^2)
## Likelihood Ratio 353.36 16        0
## Pearson          530.16 16        0
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.741 
## Cramer's V        : 0.551

Fisher’s Exact Test proves that this association is indeed statistically significant since p-value < 2.2e-16. Effect size is rather large (Cramer’s V = 0.551). This proves the conclusions made before.

Next variables to be analysed are Curve and Aperture. While previous observations show that Curve and Bent are correlated, we first map Curve and Aperture against each other:

curve_aperture_data  <- dict_output[, c(3, 4)]
CA.contingency_table <- table(curve_aperture_data$H1.Aperture, curve_aperture_data$H1.Curve)
CA.res.ca =  CA(CA.contingency_table)

Afterwards, we add Bent into the picture. Correlation is again visible:

curve_bent_aperture_data <- dict_output[, c(3, 4, 5)]
BA.contingency_table <- table(curve_aperture_data$H1.Aperture, curve_bent_data$H1.Bent)
CBA.contingency_table <- cbind(CA.contingency_table, BA.contingency_table)
CBA.res.ca = CA(CBA.contingency_table, col.sup=6:ncol(CBA.contingency_table))

Here, the top node Finger Selection is plotted against its dependent nodes under the within the category of hand configuration: Aperture, Curve, and Width. Some correlation is expected between the top node and its dependents.

fing.sel_aperture_data <- dict_output[, c(2, 3)]
FA.contingency_table <- table(fing.sel_aperture_data$H1.FingerSelection, fing.sel_aperture_data$H1.Aperture)
FA.res.ca =  CA(FA.contingency_table, graph=FALSE)
FA.contingency_table
##                    
##                     absent closed closed-open open open-closed
##   1-st                  75     16           6    8           8
##   1-st; 2-nd            42      7           2    0           3
##   1-st; 2-nd; 3-rd       2      0           1    0           0
##   1-st; 2-nd; thumb      1      0           0    0           0
##   1-st; 4-th             7      0           0    0           0
##   1-st; thumb           11      0           0    0           0
##   2-nd                   2      0           2    0           0
##   3-rd                   0      1           0    0           0
##   absent                33      0           0    0           1
##   all                  135     11           8   11          30
##   all; thumb             0      0           0    0           1
##   thumb                  7      0           0    0           0
##   thumb; 4-th            5      0           0    0           0
fing.sel_curve_data <- dict_output[, c(2, 4)]
FC.contingency_table <- table(fing.sel_curve_data$H1.FingerSelection, fing.sel_curve_data$H1.Curve)
FC.res.ca =  CA(FC.contingency_table, graph=FALSE)
FC.contingency_table
##                    
##                     absent curved curved-straight straight straight-curved
##   1-st                   2     27               4       70              10
##   1-st; 2-nd             0     10               2       37               5
##   1-st; 2-nd; 3-rd       0      0               1        2               0
##   1-st; 2-nd; thumb      0      0               0        1               0
##   1-st; 4-th             0      0               0        7               0
##   1-st; thumb            0      9               0        2               0
##   2-nd                   0      2               0        2               0
##   3-rd                   0      1               0        0               0
##   absent                31      0               0        3               0
##   all                    9     16               6      145              19
##   all; thumb             0      0               0        1               0
##   thumb                  1      0               0        6               0
##   thumb; 4-th            0      0               0        5               0
fing.sel_width_data <- dict_output[, c(2, 8)]
FW.contingency_table <- table(fing.sel_width_data$H1.FingerSelection, fing.sel_width_data$H1.Width)
FW.res.ca =  CA(FW.contingency_table, graph=FALSE)
FW.contingency_table
##                    
##                     absent pointed pointed-wide pointed; pointed-wide wide
##   1-st                 112       1            0                     0    0
##   1-st; 2-nd             0      19            2                     0   31
##   1-st; 2-nd; 3-rd       0       0            1                     0    2
##   1-st; 2-nd; thumb      0       0            0                     0    1
##   1-st; 4-th             7       0            0                     0    0
##   1-st; thumb           10       1            0                     0    0
##   2-nd                   3       1            0                     0    0
##   3-rd                   1       0            0                     0    0
##   absent                31       1            0                     0    1
##   all                    6     131            5                     1   38
##   all; thumb             0       1            0                     0    0
##   thumb                  7       0            0                     0    0
##   thumb; 4-th            5       0            0                     0    0
##                    
##                     wide-pointed
##   1-st                         0
##   1-st; 2-nd                   2
##   1-st; 2-nd; 3-rd             0
##   1-st; 2-nd; thumb            0
##   1-st; 4-th                   0
##   1-st; thumb                  0
##   2-nd                         0
##   3-rd                         0
##   absent                       1
##   all                         14
##   all; thumb                   0
##   thumb                        0
##   thumb; 4-th                  0

Multiple correspondence analysis is carried out for hand configuration factors.

hand.configuration_data <- dict_output[, c(2, 3, 4, 8)]
cats = apply(hand.configuration_data, 2, function(x) nlevels(as.factor(x)))
HCmca = MCA(hand.configuration_data, graph = FALSE)
HCeig <- HCmca$eig

library("corrplot")
## corrplot 0.84 loaded
hand.configuration_data <- dict_output[, c(2, 3, 4, 8)]
HCmca = MCA(hand.configuration_data, graph = FALSE, method = "burt")
summary(HCmca)
## 
## Call:
## MCA(X = hand.configuration_data, graph = FALSE, method = "burt") 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6
## Variance               0.390   0.314   0.208   0.196   0.123   0.112
## % of var.             18.321  14.776   9.795   9.200   5.773   5.246
## Cumulative % of var.  18.321  33.098  42.893  52.093  57.867  63.112
##                        Dim.7   Dim.8   Dim.9  Dim.10  Dim.11  Dim.12
## Variance               0.083   0.074   0.068   0.066   0.064   0.063
## % of var.              3.893   3.458   3.180   3.094   2.999   2.938
## Cumulative % of var.  67.005  70.463  73.644  76.738  79.737  82.674
##                       Dim.13  Dim.14  Dim.15  Dim.16  Dim.17  Dim.18
## Variance               0.062   0.062   0.058   0.055   0.044   0.032
## % of var.              2.937   2.913   2.744   2.588   2.061   1.509
## Cumulative % of var.  85.612  88.525  91.269  93.857  95.918  97.427
##                       Dim.19  Dim.20  Dim.21  Dim.22  Dim.23  Dim.24
## Variance               0.022   0.012   0.009   0.008   0.003   0.001
## % of var.              1.042   0.555   0.418   0.373   0.119   0.059
## Cumulative % of var.  98.469  99.024  99.442  99.815  99.934  99.993
##                       Dim.25
## Variance               0.000
## % of var.              0.007
## Cumulative % of var. 100.000
## 
## Individuals (the 10 first)
##                                         Dim.1    ctr   cos2    Dim.2
## 1                                    | -0.152  0.008  0.000 |  1.025
## 2                                    | -0.109  0.004  0.004 | -0.403
## 3                                    | -0.141  0.007  0.011 | -0.460
## 4                                    | -0.173  0.011  0.006 | -0.948
## 5                                    | -0.127  0.006  0.012 |  0.555
## 6                                    | -0.127  0.006  0.012 |  0.555
## 7                                    |  1.698  1.060  0.084 |  0.758
## 8                                    | -0.137  0.007  0.021 |  0.048
## 9                                    | -0.205  0.015  0.013 | -1.006
## 10                                   | -0.214  0.017  0.008 |  1.617
##                                         ctr   cos2    Dim.3    ctr   cos2
## 1                                     0.430  0.009 | -2.185  2.399  0.042
## 2                                     0.066  0.050 | -0.289  0.042  0.026
## 3                                     0.087  0.119 | -0.051  0.001  0.001
## 4                                     0.368  0.194 |  0.218  0.024  0.010
## 5                                     0.126  0.238 | -0.285  0.041  0.063
## 6                                     0.126  0.238 | -0.285  0.041  0.063
## 7                                     0.235  0.017 | -0.836  0.351  0.020
## 8                                     0.001  0.003 |  0.019  0.000  0.000
## 9                                     0.414  0.318 |  0.455  0.104  0.065
## 10                                    1.069  0.460 |  1.545  1.199  0.420
##                                       
## 1                                    |
## 2                                    |
## 3                                    |
## 4                                    |
## 5                                    |
## 6                                    |
## 7                                    |
## 8                                    |
## 9                                    |
## 10                                   |
## 
## Categories (the 10 first)
##                                          Dim.1     ctr    cos2  v.test  
## H1.FingerSelection_1-st              |   0.014   0.003   0.000   0.170 |
## H1.FingerSelection_1-st; 2-nd        |   0.067   0.036   0.002   0.528 |
## H1.FingerSelection_1-st; 2-nd; 3-rd  |   2.608   3.002   0.173   4.528 |
## H1.FingerSelection_1-st; 2-nd; thumb |  -0.227   0.008   0.000  -0.227 |
## H1.FingerSelection_1-st; 4-th        |  -0.220   0.050   0.003  -0.587 |
## H1.FingerSelection_1-st; thumb       |  -0.185   0.055   0.003  -0.620 |
## H1.FingerSelection_2-nd              |   0.967   0.550   0.033   1.940 |
## H1.FingerSelection_3-rd              |  -0.152   0.003   0.000  -0.152 |
## H1.FingerSelection_absent            |  -0.219   0.240   0.009  -1.327 |
## H1.FingerSelection_all               |  -0.013   0.005   0.000  -0.243 |
##                                        Dim.2     ctr    cos2  v.test  
## H1.FingerSelection_1-st                0.564   6.566   0.289   6.963 |
## H1.FingerSelection_1-st; 2-nd         -0.442   1.924   0.090  -3.466 |
## H1.FingerSelection_1-st; 2-nd; 3-rd   -0.302   0.050   0.002  -0.525 |
## H1.FingerSelection_1-st; 2-nd; thumb  -0.371   0.025   0.001  -0.371 |
## H1.FingerSelection_1-st; 4-th          0.547   0.382   0.019   1.456 |
## H1.FingerSelection_1-st; thumb         0.808   1.311   0.060   2.712 |
## H1.FingerSelection_2-nd                0.496   0.179   0.009   0.995 |
## H1.FingerSelection_3-rd                1.025   0.192   0.009   1.025 |
## H1.FingerSelection_absent              1.487  13.703   0.430   9.017 |
## H1.FingerSelection_all                -0.571  11.582   0.640 -10.706 |
##                                        Dim.3     ctr    cos2  v.test  
## H1.FingerSelection_1-st               -0.419   5.445   0.159  -5.163 |
## H1.FingerSelection_1-st; 2-nd         -0.296   1.303   0.040  -2.322 |
## H1.FingerSelection_1-st; 2-nd; 3-rd    0.050   0.002   0.000   0.087 |
## H1.FingerSelection_1-st; 2-nd; thumb  -0.280   0.022   0.001  -0.280 |
## H1.FingerSelection_1-st; 4-th         -0.124   0.030   0.001  -0.332 |
## H1.FingerSelection_1-st; thumb        -0.930   2.618   0.079  -3.121 |
## H1.FingerSelection_2-nd               -0.602   0.399   0.013  -1.209 |
## H1.FingerSelection_3-rd               -2.185   1.314   0.042  -2.185 |
## H1.FingerSelection_absent              1.510  21.325   0.443   9.158 |
## H1.FingerSelection_all                 0.137   1.007   0.037   2.570 |
## 
## Categorical variables (eta2)
##                                        Dim.1 Dim.2 Dim.3  
## H1.FingerSelection                   | 0.101 0.834 0.616 |
## H1.Aperture                          | 0.834 0.180 0.320 |
## H1.Curve                             | 0.843 0.443 0.708 |
## H1.Width                             | 0.720 0.786 0.182 |
corrplot(HCmca$var$contrib, is.corr = FALSE)

plot(HCmca, invisible = c("ind"), cex=.8, selectMod = "contrib 10")

plot(HCmca, invisible = c("ind"), cex=.8, selectMod = "cos2 10")

Finger Selection seems to be correlated with Curve and Width, but not with Aperture. Therefore, we carry out Fisher’s Tests:

#FinSel~Aperture
fisher.test(FA.contingency_table, simulate.p.value = TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  FA.contingency_table
## p-value = 0.009995
## alternative hypothesis: two.sided
#FinSel~Curve
fisher.test(FC.contingency_table, simulate.p.value = TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  FC.contingency_table
## p-value = 0.0004998
## alternative hypothesis: two.sided
assocstats(FC.contingency_table)
##                     X^2 df P(> X^2)
## Likelihood Ratio 226.55 48        0
## Pearson          357.76 48        0
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.671 
## Cramer's V        : 0.453
#FinSel~Width
fisher.test(FW.contingency_table, simulate.p.value = TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  FW.contingency_table
## p-value = 0.0004998
## alternative hypothesis: two.sided
assocstats(FW.contingency_table)
##                     X^2 df P(> X^2)
## Likelihood Ratio 540.93 60        0
## Pearson          467.89 60        0
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.719 
## Cramer's V        : 0.463

Tests support our hypotheses: indeed, for Finger Selection and Aperture, the null hypothesis postulating absence of relationship cannot be rejected since p-value is greater than 0.001. The other two pairs show some correlation, and the effect is quite strong (Cramer’s V equalling 0.453 and 0.463) in both cases.

Analysing Finger Selection even more, we come to unexpected (yet explainable from the theoretical point of view) conclusions. Here, the first two dimensions reflect most of the variation:

## 
## Call:
## CA(X = FC.contingency_table, graph = FALSE) 
## 
## The chi square of independence between the two variables is equal to 357.7588 (p-value =  5.880526e-49 ).
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4
## Variance               0.637   0.151   0.024   0.009
## % of var.             77.583  18.385   2.929   1.104
## Cumulative % of var.  77.583  95.967  98.896 100.000
## 
## Rows (the 10 first)
##                     Iner*1000     Dim.1     ctr    cos2     Dim.2     ctr
## 1-st              |    32.136 |  -0.283   3.263   0.646 |   0.204   7.147
## 1-st; 2-nd        |    14.171 |  -0.334   2.170   0.975 |   0.040   0.132
## 1-st; 2-nd; 3-rd  |    23.505 |  -0.324   0.113   0.031 |  -0.489   1.092
## 1-st; 2-nd; thumb |     1.265 |  -0.298   0.032   0.161 |  -0.497   0.376
## 1-st; 4-th        |     8.856 |  -0.298   0.224   0.161 |  -0.497   2.632
## 1-st; thumb       |    89.351 |  -0.422   0.707   0.050 |   1.828  55.905
## 2-nd              |     9.769 |  -0.374   0.201   0.131 |   0.924   5.191
## 3-rd              |    13.091 |  -0.450   0.073   0.035 |   2.345   8.361
## absent            |   580.279 |   2.726  91.036   0.999 |   0.097   0.484
## all               |    34.963 |  -0.165   1.912   0.348 |  -0.223  14.685
##                      cos2     Dim.3     ctr    cos2  
## 1-st                0.336 |   0.035   1.289   0.010 |
## 1-st; 2-nd          0.014 |   0.026   0.358   0.006 |
## 1-st; 2-nd; 3-rd    0.070 |   1.698  82.580   0.844 |
## 1-st; 2-nd; thumb   0.448 |  -0.275   0.722   0.137 |
## 1-st; 4-th          0.448 |  -0.275   5.057   0.137 |
## 1-st; thumb         0.944 |  -0.064   0.435   0.001 |
## 2-nd                0.802 |  -0.146   0.818   0.020 |
## 3-rd                0.964 |  -0.018   0.003   0.000 |
## absent              0.001 |   0.013   0.052   0.000 |
## all                 0.634 |  -0.021   0.815   0.006 |
## 
## Columns
##                     Iner*1000     Dim.1     ctr    cos2     Dim.2     ctr
## absent            |   572.500 |   2.409  89.874   0.999 |   0.060   0.235
## curved            |   142.912 |  -0.359   3.019   0.134 |   0.911  81.989
## curved-straight   |    26.615 |  -0.300   0.422   0.101 |  -0.184   0.668
## straight          |    62.408 |  -0.238   5.714   0.583 |  -0.193  15.936
## straight-curved   |    16.112 |  -0.281   0.970   0.383 |  -0.151   1.172
##                      cos2     Dim.3     ctr    cos2  
## absent              0.001 |   0.006   0.016   0.000 |
## curved              0.865 |  -0.003   0.005   0.000 |
## curved-straight     0.038 |   0.875  95.026   0.858 |
## straight            0.385 |  -0.043   4.879   0.019 |
## straight-curved     0.110 |   0.015   0.075   0.001 |

The most notable evidence here is that absence of fingers selected is correlated with absence of a curve, and all fingers selected are connected with a straight hand (incidentally yielding an open palm which is a common sign in sign languages).

Looking at the points best located in the new space presents us with the following plots:

The observations made before are supported. What is more, relationship is observed between the presence of a curve and the selection of a single third (middle) finger. The reason for this may be the taboo nature of showing a straight middle finger; this way, it can be the only finger selected only when it is curved.

Finger Selection and Width have the first two dimensions contribute 97.1% to the inertia:

summary(FW.res.ca)
## 
## Call:
## CA(X = FW.contingency_table, graph = FALSE) 
## 
## The chi square of independence between the two variables is equal to 467.8905 (p-value =  1.636154e-64 ).
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5
## Variance               0.895   0.147   0.029   0.002   0.000
## % of var.             83.393  13.730   2.683   0.186   0.008
## Cumulative % of var.  83.393  97.122  99.806  99.992 100.000
## 
## Rows (the 10 first)
##                         Iner*1000     Dim.1     ctr    cos2     Dim.2
## 1-st                  |   350.822 |  -1.163  39.179   0.999 |   0.019
## 1-st; 2-nd            |   176.678 |   0.865  10.351   0.524 |   0.805
## 1-st; 2-nd; 3-rd      |    53.051 |   0.896   0.617   0.104 |   1.873
## 1-st; 2-nd; thumb     |    11.405 |   0.889   0.202   0.159 |   1.901
## 1-st; 4-th            |    22.406 |  -1.181   2.502   0.999 |   0.027
## 1-st; thumb           |    25.307 |  -0.998   2.808   0.993 |  -0.059
## 2-nd                  |     4.801 |  -0.678   0.471   0.878 |  -0.209
## 3-rd                  |     3.201 |  -1.181   0.357   0.999 |   0.027
## absent                |    79.642 |  -1.004   8.778   0.986 |   0.029
## all                   |   303.261 |   0.778  30.268   0.893 |  -0.268
##                           ctr    cos2     Dim.3     ctr    cos2  
## 1-st                    0.062   0.000 |   0.004   0.012   0.000 |
## 1-st; 2-nd             54.438   0.454 |  -0.176  13.268   0.022 |
## 1-st; 2-nd; 3-rd       16.389   0.455 |   1.843  81.188   0.441 |
## 1-st; 2-nd; thumb       5.624   0.727 |  -0.746   4.435   0.112 |
## 1-st; 4-th              0.008   0.001 |   0.004   0.001   0.000 |
## 1-st; thumb             0.059   0.003 |   0.002   0.000   0.000 |
## 2-nd                    0.271   0.083 |  -0.001   0.000   0.000 |
## 3-rd                    0.001   0.001 |   0.004   0.000   0.000 |
## absent                  0.044   0.001 |  -0.020   0.110   0.000 |
## all                    21.781   0.106 |   0.025   0.983   0.001 |
## 
## Columns
##                         Iner*1000     Dim.1     ctr    cos2     Dim.2
## absent                |   521.025 |  -1.117  58.215   1.000 |   0.010
## pointed               |   264.299 |   0.787  24.592   0.833 |  -0.352
## pointed-wide          |    48.603 |   0.861   1.520   0.280 |   0.698
## pointed; pointed-wide |     2.835 |   0.823   0.173   0.548 |  -0.698
## wide                  |   210.160 |   0.841  13.224   0.563 |   0.730
## wide-pointed          |    26.222 |   0.723   2.275   0.776 |  -0.324
##                           ctr    cos2     Dim.3     ctr    cos2  
## absent                  0.031   0.000 |   0.001   0.001   0.000 |
## pointed                29.880   0.167 |  -0.003   0.010   0.000 |
## pointed-wide            6.068   0.184 |   1.192  90.486   0.536 |
## pointed; pointed-wide   0.758   0.394 |   0.148   0.175   0.018 |
## wide                   60.492   0.424 |  -0.127   9.323   0.013 |
## wide-pointed            2.771   0.156 |  -0.007   0.006   0.000 |

Wide and pointed values of width are juxtaposed and contribute quite a lot of the inertia along the second dimension.

The choice of one finger or fingers that are not next to each other is correlated with the absence of Width. The selection of all fingers is connected to the pointed (neutral) Width, meaning that all fingers tend to be pushed towards each other rather than open like a fan. The value “wide”, in turn, is common for selection of the thumb and index finger which are often put far apart:

Next, correspondence between Focus Orientation and Facing Orientation is presented:

facing_focus_data <- dict_output[, c(6, 7)]
FF.contingency_table <- table(facing_focus_data$H1.Facing, facing_focus_data$H1.Focus)
FF.res.ca =  CA(FF.contingency_table)

The following calculations plot three variables related to orientation - Focus, Facing and Dynamic Orientation - against each other. Facing shows stronger correlation; in the third map, Focus is mapped over Dynamic and Facing.

orientation_focus_data <- dict_output[, c(7, 9)]
OF1.contingency_table <- table(orientation_focus_data$Dynamic.Orientation, orientation_focus_data$H1.Focus)
OF1.res.ca =  CA(OF1.contingency_table)

orientation_facing_data <- dict_output[, c(6, 9)]
OF2.contingency_table <- table(orientation_facing_data$Dynamic.Orientation, orientation_facing_data$H1.Facing)
OF2.res.ca =  CA(OF2.contingency_table)

OFF.contingency_table <- cbind(OF2.contingency_table, OF1.contingency_table)
OFF.res.ca = CA(OFF.contingency_table, col.sup=8:ncol(OFF.contingency_table))

Multiple correspondence analysis for the bunch of orientation-related nodes yields the following results:

orientation_data <- dict_output[, c(6, 7, 9)]
OFFmca = MCA(orientation_data, graph = FALSE, method = "burt")
summary(OFFmca)
## 
## Call:
## MCA(X = orientation_data, graph = FALSE, method = "burt") 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6
## Variance               0.344   0.205   0.187   0.160   0.155   0.139
## % of var.             13.693   8.147   7.438   6.364   6.167   5.534
## Cumulative % of var.  13.693  21.839  29.277  35.641  41.807  47.341
##                        Dim.7   Dim.8   Dim.9  Dim.10  Dim.11  Dim.12
## Variance               0.136   0.129   0.125   0.112   0.109   0.102
## % of var.              5.414   5.153   4.973   4.474   4.353   4.069
## Cumulative % of var.  52.756  57.909  62.881  67.355  71.708  75.777
##                       Dim.13  Dim.14  Dim.15  Dim.16  Dim.17  Dim.18
## Variance               0.100   0.092   0.089   0.078   0.075   0.061
## % of var.              3.972   3.663   3.547   3.100   2.974   2.432
## Cumulative % of var.  79.748  83.411  86.958  90.058  93.032  95.464
##                       Dim.19  Dim.20  Dim.21
## Variance               0.051   0.041   0.022
## % of var.              2.021   1.633   0.881
## Cumulative % of var.  97.485  99.119 100.000
## 
## Individuals (the 10 first)
##                     Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3
## 1                | -0.319  0.040  0.022 | -0.022  0.000  0.000 |  0.314
## 2                | -0.268  0.028  0.027 |  0.942  0.449  0.327 |  0.331
## 3                | -0.152  0.009  0.008 |  0.426  0.092  0.061 |  0.207
## 4                |  0.667  0.174  0.059 |  0.191  0.018  0.005 | -0.240
## 5                | -0.268  0.028  0.027 |  0.942  0.449  0.327 |  0.331
## 6                | -0.047  0.001  0.000 | -0.824  0.344  0.134 |  0.844
## 7                | -0.169  0.011  0.009 | -0.233  0.028  0.017 | -0.102
## 8                | -0.047  0.001  0.000 | -0.824  0.344  0.134 |  0.844
## 9                | -0.294  0.034  0.014 |  0.567  0.163  0.053 |  0.452
## 10               | -0.285  0.032  0.027 |  0.282  0.040  0.027 |  0.022
##                     ctr   cos2  
## 1                 0.052  0.021 |
## 2                 0.058  0.040 |
## 3                 0.023  0.014 |
## 4                 0.031  0.008 |
## 5                 0.058  0.040 |
## 6                 0.378  0.140 |
## 7                 0.006  0.003 |
## 8                 0.378  0.140 |
## 9                 0.108  0.034 |
## 10                0.000  0.000 |
## 
## Categories (the 10 first)
##                     Dim.1    ctr   cos2 v.test    Dim.2    ctr   cos2
## H1.Facing_absent |  2.359 33.375  0.808 12.639 | -0.309  0.962  0.014
## H1.Facing_back   | -0.345  1.108  0.037 -2.346 | -0.287  1.294  0.026
## H1.Facing_palm   | -0.083  0.217  0.010 -1.203 |  0.397  8.371  0.218
## H1.Facing_radial | -0.129  0.121  0.004 -0.767 | -0.112  0.154  0.003
## H1.Facing_root   | -0.007  0.000  0.000 -0.036 |  1.416 18.715  0.344
## H1.Facing_tips   | -0.113  0.318  0.013 -1.388 | -0.498 10.470  0.248
## H1.Facing_ulnar  | -0.376  1.695  0.057 -2.947 | -0.212  0.905  0.018
## H1.Focus_absent  |  1.526 20.171  0.563  9.973 |  0.361  1.898  0.032
## H1.Focus_back    | -0.151  0.247  0.008 -1.119 | -0.427  3.329  0.068
## H1.Focus_palm    | -0.165  0.381  0.013 -1.414 |  0.871 17.841  0.362
##                  v.test    Dim.3    ctr   cos2 v.test  
## H1.Facing_absent -1.655 |  0.270  0.804  0.011  1.446 |
## H1.Facing_back   -1.956 | -0.187  0.600  0.011 -1.272 |
## H1.Facing_palm    5.759 |  0.113  0.740  0.018  1.636 |
## H1.Facing_radial -0.667 |  0.270  0.981  0.018  1.609 |
## H1.Facing_root    7.283 | -0.218  0.486  0.008 -1.121 |
## H1.Facing_tips   -6.144 | -0.288  3.821  0.083 -3.547 |
## H1.Facing_ulnar  -1.661 |  0.251  1.396  0.026  1.971 |
## H1.Focus_absent   2.360 | -0.572  5.212  0.079 -3.736 |
## H1.Focus_back    -3.166 | -0.262  1.379  0.026 -1.947 |
## H1.Focus_palm     7.464 |  0.326  2.736  0.051  2.793 |
## 
## Categorical variables (eta2)
##                       Dim.1 Dim.2 Dim.3  
## H1.Facing           | 0.648 0.555 0.114 |
## H1.Focus            | 0.431 0.426 0.566 |
## Dynamic.Orientation | 0.681 0.377 0.617 |
corrplot(OFFmca$var$contrib, is.corr = FALSE)

plot(OFFmca, invisible = c("ind"), cex=.8, selectMod = "contrib 10")

plot(OFFmca, invisible = c("ind"), cex=.8, selectMod = "cos2 10")

A possible conclusion here would be that dynamic orientations are often clustered around the extremes. Checking our initial expectation, we apply Fisher’s Exact Test to the pair of Facing and Dynamic Orientation:

fisher.test(OF2.contingency_table, simulate.p.value = TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  OF2.contingency_table
## p-value = 0.0004998
## alternative hypothesis: two.sided
assocstats(OF2.contingency_table)
##                     X^2 df   P(> X^2)
## Likelihood Ratio 113.19 54 4.4055e-06
## Pearson          167.28 54 1.6243e-13
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.527 
## Cramer's V        : 0.253

Some correlation is present (p-value is below the threshold 0.001), yet, the effect size is small (Cramer’s V = 0.282).

Aperture and Focus show some slight correlation; however, values of both variables are spread rather evenly across the quarters:

aperture_focus_data <- dict_output[, c(3, 7)]
AP.contingency_table <- table(aperture_focus_data$H1.Aperture, aperture_focus_data$H1.Focus)
AP.res.ca = CA(AP.contingency_table)

The plot for Curve and Focus correspondence analysis looks similarly evenly spread:

curve_focus_data <- dict_output[, c(4, 7)]
CF.contingency_table <- table(curve_focus_data$H1.Curve, curve_focus_data$H1.Focus)
CF.res.ca = CA(CF.contingency_table)

Finally, MCA is performed for Aperture, Curve, and Focus. Aperture and Curve show strong correlation:

hand.configuration_focus_data <- dict_output[, c(3, 4, 7)]
HCFmca = MCA(hand.configuration_focus_data, graph = FALSE, method = "burt")
summary(HCFmca)
## 
## Call:
## MCA(X = hand.configuration_focus_data, graph = FALSE, method = "burt") 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6
## Variance               0.389   0.279   0.229   0.191   0.134   0.122
## % of var.             21.001  15.073  12.338  10.315   7.246   6.571
## Cumulative % of var.  21.001  36.074  48.412  58.727  65.974  72.545
##                        Dim.7   Dim.8   Dim.9  Dim.10  Dim.11  Dim.12
## Variance               0.115   0.111   0.097   0.068   0.053   0.032
## % of var.              6.183   5.997   5.239   3.677   2.881   1.711
## Cumulative % of var.  78.728  84.725  89.964  93.641  96.523  98.233
##                       Dim.13  Dim.14
## Variance               0.029   0.003
## % of var.              1.585   0.181
## Cumulative % of var.  99.819 100.000
## 
## Individuals (the 10 first)
##                             Dim.1    ctr   cos2    Dim.2    ctr   cos2  
## 1                        |  0.034  0.000  0.000 | -1.466  0.933  0.269 |
## 2                        | -0.258  0.025  0.029 |  0.119  0.006  0.006 |
## 3                        | -0.173  0.011  0.012 | -0.286  0.036  0.032 |
## 4                        | -0.347  0.044  0.018 |  1.438  0.897  0.312 |
## 5                        | -0.258  0.025  0.029 |  0.119  0.006  0.006 |
## 6                        | -0.316  0.037  0.023 | -0.524  0.119  0.063 |
## 7                        |  1.834  1.237  0.293 | -0.620  0.167  0.034 |
## 8                        | -0.316  0.037  0.023 | -0.524  0.119  0.063 |
## 9                        | -0.325  0.039  0.020 |  0.898  0.350  0.155 |
## 10                       | -0.335  0.041  0.022 |  0.127  0.007  0.003 |
##                           Dim.3    ctr   cos2  
## 1                         1.134  0.617  0.161 |
## 2                        -0.525  0.132  0.121 |
## 3                        -0.538  0.139  0.113 |
## 4                         0.531  0.135  0.043 |
## 5                        -0.525  0.132  0.121 |
## 6                        -0.252  0.030  0.015 |
## 7                         0.606  0.176  0.032 |
## 8                        -0.252  0.030  0.015 |
## 9                         0.337  0.054  0.022 |
## 10                       -0.640  0.196  0.080 |
## 
## Categories (the 10 first)
##                              Dim.1     ctr    cos2  v.test     Dim.2
## H1.Aperture_absent       |  -0.160   1.614   0.170  -5.551 |  -0.013
## H1.Aperture_closed       |   0.064   0.028   0.001   0.395 |  -0.901
## H1.Aperture_closed-open  |   3.435  44.020   0.951  15.291 |   0.440
## H1.Aperture_open         |  -0.209   0.163   0.005  -0.931 |  -1.334
## H1.Aperture_open-closed  |  -0.285   0.685   0.023  -1.965 |   1.222
## H1.Curve_absent          |  -0.253   0.539   0.019  -1.743 |   0.028
## H1.Curve_curved          |   0.052   0.035   0.001   0.457 |  -0.967
## H1.Curve_curved-straight |   4.177  44.547   0.950  15.273 |   0.549
## H1.Curve_straight        |  -0.109   0.662   0.057  -3.075 |   0.016
## H1.Curve_straight-curved |  -0.473   1.492   0.046  -2.867 |   1.470
##                              ctr    cos2  v.test     Dim.3     ctr    cos2
## H1.Aperture_absent         0.014   0.001  -0.438 |  -0.318  10.841   0.670
## H1.Aperture_closed         7.777   0.191  -5.552 |   0.870   8.850   0.178
## H1.Aperture_closed-open    1.007   0.016   1.959 |   0.112   0.079   0.001
## H1.Aperture_open           9.248   0.211  -5.937 |   1.569  15.629   0.292
## H1.Aperture_open-closed   17.583   0.416   8.433 |   0.919  12.133   0.235
## H1.Curve_absent            0.009   0.000   0.193 |  -0.466   3.118   0.066
## H1.Curve_curved           16.620   0.410  -8.439 |   0.910  17.974   0.363
## H1.Curve_curved-straight   1.071   0.016   2.006 |   0.108   0.051   0.001
## H1.Curve_straight          0.020   0.001   0.450 |  -0.302   8.555   0.433
## H1.Curve_straight-curved  20.115   0.443   8.919 |   1.303  19.297   0.348
##                           v.test  
## H1.Aperture_absent       -11.028 |
## H1.Aperture_closed         5.359 |
## H1.Aperture_closed-open    0.497 |
## H1.Aperture_open           6.983 |
## H1.Aperture_open-closed    6.338 |
## H1.Curve_absent           -3.213 |
## H1.Curve_curved            7.940 |
## H1.Curve_curved-straight   0.396 |
## H1.Curve_straight         -8.475 |
## H1.Curve_straight-curved   7.903 |
## 
## Categorical variables (eta2)
##                            Dim.1 Dim.2 Dim.3  
## H1.Aperture              | 0.871 0.565 0.682 |
## H1.Curve                 | 0.885 0.600 0.703 |
## H1.Focus                 | 0.116 0.421 0.050 |
corrplot(HCFmca$var$contrib, is.corr = FALSE)

plot(HCFmca, invisible = c("ind"), cex=.8, selectMod = "contrib 10")

plot(HCFmca, invisible = c("ind"), cex=.8, selectMod = "cos2 10")

This leads to testing the null hypothesis defying any relationship between the two values using Fisher’s Exact Test (again, chi-square is not recommended):

fisher.test(CA.contingency_table, simulate.p.value = TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  CA.contingency_table
## p-value = 0.0004998
## alternative hypothesis: two.sided
assocstats(CA.contingency_table)
##                     X^2 df P(> X^2)
## Likelihood Ratio 193.22 16        0
## Pearson          431.71 16        0
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.705 
## Cramer's V        : 0.498

As we expected, the association proves significant and the null hypothesis is rejected since p-value is below 0.001. The effect size is again considerable (Cramer’s V = 0.498).

We again look at the data in more detail now:

summary(CA.res.ca)
## 
## Call:
## CA(X = CA.contingency_table) 
## 
## The chi square of independence between the two variables is equal to 431.7059 (p-value =  8.075511e-82 ).
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4
## Variance               0.677   0.184   0.129   0.000
## % of var.             68.338  18.630  13.022   0.010
## Cumulative % of var.  68.338  86.968  99.990 100.000
## 
## Rows
##                   Iner*1000     Dim.1     ctr    cos2     Dim.2     ctr
## absent          |    63.013 |  -0.180   3.498   0.376 |  -0.218  18.834
## closed          |    73.661 |  -0.128   0.193   0.018 |   0.869  32.844
## closed-open     |   646.781 |   3.852  95.569   1.000 |  -0.037   0.032
## open            |    83.896 |  -0.111   0.079   0.006 |   1.336  42.185
## open-closed     |   122.800 |  -0.213   0.661   0.036 |   0.338   6.104
##                    cos2     Dim.3     ctr    cos2  
## absent            0.551 |  -0.079   3.571   0.073 |
## closed            0.823 |  -0.382   9.087   0.159 |
## closed-open       0.000 |   0.035   0.040   0.000 |
## open              0.928 |  -0.355   4.258   0.065 |
## open-closed       0.092 |   1.042  83.043   0.872 |
## 
## Columns
##                   Iner*1000     Dim.1     ctr    cos2     Dim.2     ctr
## absent          |    20.084 |  -0.104   0.157   0.053 |  -0.408   8.895
## curved          |   146.782 |  -0.038   0.032   0.001 |   0.915  67.720
## curved-straight |   654.394 |   4.683  96.637   0.999 |  -0.086   0.120
## straight        |    44.202 |  -0.164   2.571   0.394 |  -0.201  14.177
## straight-curved |   124.689 |  -0.229   0.603   0.033 |   0.464   9.087
##                    cos2     Dim.3     ctr    cos2  
## absent            0.817 |  -0.160   1.963   0.126 |
## curved            0.851 |  -0.381  16.788   0.147 |
## curved-straight   0.000 |   0.096   0.215   0.000 |
## straight          0.592 |  -0.031   0.494   0.014 |
## straight-curved   0.134 |   1.154  80.540   0.833 |
plot(CA.res.ca, selectRow = "contrib 3", selectCol = "contrib 3")

plot(CA.res.ca, selectRow = "contrib 3", selectCol = "contrib 3", axes = c(2,3))

Three dimensions contribute 99.9% to the inertia. Dynamic and static positions for both variables are opposed to each other, as are two static apertures - with or without a curve.

plot(CA.res.ca, selectRow = "cos2 0.7", selectCol = "cos2 0.7")

plot(CA.res.ca, selectRow = "cos2 0.7", selectCol = "cos2 0.7", axes = c(2,3))

Again, absence of Curve is close to neutral (value “straight”) - it may be assumed that the sign do not discern between the two, especially if the aperture is absent. What is more, closed Aperture is correlated with the value “curved” of Curve; therefore, the closed Aperture can be marked as straight, and “curved” can be seen as a neutral value. “Curved-straight” can be seen as a phonetic effect of closing an aperture.

Having performed various analyses and explored the data at hand, we have come to the following conclusions:

  1. Nodes seem to be correlated within categories, and the relationship is observed between the top node and its dependents. An example is Finger Selection and Curve. Statistics do not show the direction of the relationship explicitly; however,theoretical linguistic evidence suggests that finger selection defines the curve observed in a sign. This supports the claim made by Plaskovitskaya (2018) in her course paper.

  2. Curve and Bent are strongly correlated, therefore, one of the two factors can be dropped. Curve is more udeful in future analysis as it distinguishes between bent and straight static positions.

  3. Finger Selection is correlated with Curve and Width. A notable conslusion here is the absence of a straight middle finger as the only finger selected for the sign, presumably because of its obscene connotations. Another conclusion is that, when all fingers are selected, they are normally kept close to each other; however, if only the thumb and index finger are shown, they are put further apart.

  4. Curve and Aperture are correlated. Here, “curved-straight” movement of the Curve can be treated as a phonetic effect of closing the aperture. Also, the proximity of “straight” and “absent” values of the Curve may lead to combining the two into one value.